Exact Solutions of the Vibration Modes of Circular Saw Blades

Based on exact numerical calculation of Bessel functions,the frequency equations and the mode functions of usual circular saw blades with the effects of the centrifigual force neglected are exactly solved and calculated respectively,so the exact vibration modes of the saw blades are obtained. In order to examine the correctness of the results,a certain saw blade is analysed by finite element method.The findings by the two methods show a great consistency.Additionally,it is confirmed by computation that the influence of Poisson's ratio of steel on the vibration modes of the saw blades is very small.All the findings in this paper provide a direct use for saw blade design.